How to apply a piecewise function to a list?

Question

I have created this code:

xn = {4, -4, 4, -4}
f[x_] = Piecewise[{{Sqrt[x], x >= 0}, {Sqrt[-x], x < 0}}]
f[xn]

With this code I would expect as a result:

{2,2,2,2}

But that's not what I get.

Question 1 - Why don't I get the desired result?

Question 2 - How to get the desired result?

"What's the difference" - in your notebook, highlight the /@ and press F1, so that you can answer your own question. — J. M.'s missing motivation, Jul 12 '16 at 21:11
Also note that using Set(=) does not scope the symbol x which may lead to trouble — Sascha, Jul 12 '16 at 21:12
@J.M. For some reaon Sqrt[Abs[x]] doesn't work, see: http://mathematica.stackexchange.com/questions/120577/strange-behavior-when-using-abs — GambitSquared, Jul 12 '16 at 21:29
Well, you didn't say that you were going to differentiate the blasted thing… — J. M.'s missing motivation, Jul 12 '16 at 21:58

score 3 · Accepted Answer · answered Jul 12 '16 at 22:43

Your code shows two elementary misunderstandings. First, you do not understand the difference between Set and SetDelayed. Second, you do not understand what a Listable function is. Yet both these concepts are fundamental to working with Mathematica.

An experienced Mathematica user would write your code as

xn = {4, -4, 4, -4};
f[x_] := Piecewise[{{Sqrt[x], x >= 0}, {Sqrt[-x], x < 0}}]
f /@ xn

without even having to think about it.

How to apply a piecewise function to a list?

1 Answers1